Gateaux derivativeIn mathematics, the Gateaux differential or Gateaux derivative is a generalization of the concept of directional derivative in differential calculus. Named after René Gateaux, a French mathematician who died at age 25 in World War I, it is defined for functions between locally convex topological vector spaces such as Banach spaces. Like the Fréchet derivative on a Banach space, the Gateaux differential is often used to formalize the functional derivative commonly used in the calculus of variations and physics.
Derivative workIn copyright law, a derivative work is an expressive creation that includes major copyrightable elements of a first, previously created original work (the underlying work). The derivative work becomes a second, separate work independent in form from the first. The transformation, modification or adaptation of the work must be substantial and bear its author's personality sufficiently to be original and thus protected by copyright. Translations, cinematic adaptations and musical arrangements are common types of derivative works.
Nonlinear systemIn mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems.
Elliptic operatorIn the theory of partial differential equations, elliptic operators are differential operators that generalize the Laplace operator. They are defined by the condition that the coefficients of the highest-order derivatives be positive, which implies the key property that the principal symbol is invertible, or equivalently that there are no real characteristic directions. Elliptic operators are typical of potential theory, and they appear frequently in electrostatics and continuum mechanics.
EquationIn mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. Solving an equation containing variables consists of determining which values of the variables make the equality true.
Period-doubling bifurcationIn dynamical systems theory, a period-doubling bifurcation occurs when a slight change in a system's parameters causes a new periodic trajectory to emerge from an existing periodic trajectory—the new one having double the period of the original. With the doubled period, it takes twice as long (or, in a discrete dynamical system, twice as many iterations) for the numerical values visited by the system to repeat themselves. A period-halving bifurcation occurs when a system switches to a new behavior with half the period of the original system.
Criticism of copyrightCriticism of copyright, or anti-copyright sentiment, is a dissenting view of the current state of copyright law or copyright as a concept. Critics often discuss philosophical, economical, or social rationales of such laws and the laws' implementations, the benefits of which they claim do not justify the policy's costs to society. They advocate for changing the current system, though different groups have different ideas of what that change should be.
René Maurice FréchetRené Maurice Fréchet (ʁəne mɔʁis fʁeʃɛ, moʁ-; 2 September 1878 – 4 June 1973) was a French mathematician. He made major contributions to general topology and was the first to define metric spaces. He also made several important contributions to the field of statistics and probability, as well as calculus. His dissertation opened the entire field of functionals on metric spaces and introduced the notion of compactness. Independently of Riesz, he discovered the representation theorem in the space of Lebesgue square integrable functions.
Copyright noticeIn United States copyright law, a copyright notice is a notice of statutorily prescribed form that informs users of the underlying claim to copyright ownership in a published work. Copyright is a form of protection provided by US law to authors of "original works of authorship". When a work is published under the authority of the copyright owner, a notice of copyright may be placed on all publicly distributed copies or phonorecords. The use of the notice is the responsibility of the copyright owner and does not require permission from, or registration with, the Copyright Office.
Hyperbolic partial differential equationIn mathematics, a hyperbolic partial differential equation of order is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first derivatives. More precisely, the Cauchy problem can be locally solved for arbitrary initial data along any non-characteristic hypersurface. Many of the equations of mechanics are hyperbolic, and so the study of hyperbolic equations is of substantial contemporary interest. The model hyperbolic equation is the wave equation.
Copyright symbolThe copyright symbol, or copyright sign, (a circled capital letter C for copyright), is the symbol used in copyright notices for works other than sound recordings. The use of the symbol is described by the Universal Copyright Convention. The symbol is widely recognized but, under the Berne Convention, is no longer required in most nations to assert a new copyright. In the United States, the Berne Convention Implementation Act of 1988, effective March 1, 1989, removed the requirement for the copyright symbol from U.
Copyright infringementCopyright infringement (at times referred to as piracy) is the use of works protected by copyright without permission for a usage where such permission is required, thereby infringing certain exclusive rights granted to the copyright holder, such as the right to reproduce, distribute, display or perform the protected work, or to make derivative works. The copyright holder is typically the work's creator, or a publisher or other business to whom copyright has been assigned.
